Form the data given below for the reaction:`A to B to ` Products
the rate law expression is:

Options

A. Rate=k[A][B]
B. Rate=`k[A][B]^2`
C. Rate=`k[A]^2[B]^2`
D. Rate=`k[A]^2[B]`

Answer

To derive the rate law expression for the reaction \( A \rightarrow B \rightarrow \text{Products} \), we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Reaction Components**:
- The reaction involves two reactants: A and B.
- It proceeds through an intermediate B before forming the final products.

2. **Understand the Rate Law**:
- The rate law expresses the rate of a reaction as a function of the concentration of its reactants.
- The general form of the rate law for a reaction involving reactants A and B can be written as:
\[ \text{Rate} = k [A]^m [B]^n \]
where \( k \) is the rate constant, and \( m \) and \( n \) are the orders of the reaction with respect to A and B, respectively.

3. **Determine the Orders of the Reaction**:
- If the stoichiometry of the reaction is not given, we typically assume that the order with respect to each reactant is 1 unless specified otherwise.
- Therefore, we can assume:
\[ m = 1 \quad \text{and} \quad n = 1 \]

4. **Write the Rate Law Expression**:
- Substituting the assumed values into the general rate law expression, we get:
\[ \text{Rate} = k [A]^1 [B]^1 \]
- This simplifies to:
\[ \text{Rate} = k [A] [B] \]

5. **Conclusion**:
- The rate law expression for the reaction \( A \rightarrow B \rightarrow \text{Products} \) is:
\[ \text{Rate} = k [A] [B] \]